Geoscience Reference
In-Depth Information
Chapter 7
A Microstructural Model for Soils
and Granular Materials
7.1. Introduction
The mechanical behavior of granular materials is dependent on the properties of
the grains that constitute the material. It therefore appears to be logical to establish a
reasoning framework that allows us to pass from a discontinuous medium to an
equivalent continuous medium. To achieve this goal, a methodology was created by
Jean Biarez and his collaborators [BIA 62, BIA 77, BIA 89, BIA 94]. Subsequently,
a method of classifying the representative parameters of granular materials was
developed. Two classes of parameters can be distinguished:
- the parameters representing the mechanical properties of the grains and of the
local contact law;
- the parameters describing the geometrical conditions of the grain assembly.
The geometry of the grain themselves can be defined by parameters representing the
size, shape and grain size distribution, which can generally be considered invariable.
The geometry of the arrangement, which can vary, includes a parameter expressing
the compacity (a scalar) and a parameter describing its anisotropy (a tensor).
Based on this approach linking discontinuous and equivalent continuous media,
in this chapter we present a constitutive model for the continuous medium
constructed from the inter-granular properties and from the geometry of the granular
assembly. Homogenization techniques for granular materials have been developed in
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